F. Gielsdorf, L. Grundig Technical University, Berlin, Germany. Abstract

Transcription

1 The design and management of the threedimensional alignment of rails and switches F. Gielsdorf, L. Grundig Technical University, Berlin, Germany Abstract An integrated system is described for the design of horizontal, vertical and super elevation alignments, taking into account constraints while maintaining all consistency requirements. Proposed solutions for appropriate management and analysis will be presented and evaluated on the basis of real implementations and experience. Due to the global approach, and the consistency checks, an efficient tool is made available for the best fitting alignment, and generation of railway control maps necessary for the maintenance and alignment of the construction machines. The system has been used successfully by both the Swiss (SBB) and German Railways (DB). Due to the general approach adopted, an extension was possible with respect to the design of switches, a task which can now also be solved efficiently. 1 Introduction Taking the example of rails for modern high speed trains, the requirements for reliable data management of sensitive and redundant data are now outlined. This task is an excellent demonstration of the synthesis of high precision and reliable geometric information together with descriptive information. Additionally, it illustrates the key role surveying engineers play in liasing between the various professions active in this interdisciplinary area. Geodetic information systems for railways cover the areas of system planning and design, as well as the task of information retrieval and archiving. It is clear that surveying provides the basic information common to each of the individual interdisciplinary areas. This becomes even more evident when the areas are examined in detail. For example, train time schedules depend on the alignment curvature as well as the actual condition of the rails. This is because

2 72 Computers in Railways deviations of the real alignment from that planned require the allowable speed to be reduced. In the past, information for planning was considered more important than that required for maintenance. Indeed, even today many companies engaged in the provision of railway surveying systems still advertize their products almost wholy with respect to their planning capabilities. In reality it is much more important to be able to maintain existing systems, a situation especially true of densely populated areas due to the many planning restrictions. In general continuous track monitoring is needed, and additionally a reconstitution of the planned state at least every two years. Due to the increasing speed of modern trains, the larger forces acting on the rails and switches have resulted in an increase in the importance of realignment. The basic requirements for dealing with the tasks described above are the availability of the following systems: Geodetic measurement processing; Automated determination of the elements of an existing track alignment; Track alignment and track optimization; Track management and control. In this paper only the last two points are addressed. 2 Horizontal and Vertical Alignment as an Adjustment Problem The task of optimization is best described as follows: Find those parameter values for a given sequence of alignment elements, such that the alignment points will be at given distances from a number of given constraining points, within predefined tolerances; (See Griindig 1981). In the conventional technique for parameter optimization with respect to constraint points, one starts with a set of elements, and checks the constraint points one by one. If they do not fit, local elemental changes are allowed introducing "buffer" elements. Because the most influential parameters are rarely those close to the constraining points, this strategy is far from optimal. An adjustment approach allows for a change of all parameters while simultaneously enforcing constraints together with the tolerance of the constraining points. In order to formulate the optimisation problem in a general way, necessary and sufficient parameters for each alignment element are first identified. Doing so automatically, the smoothness of the alignment is guaranteed. Geometrical conditions can then be set up, formulating the fact that starting from one point the alignment eventually passes a given endpoint with a given tangential bearing. Such geometrical conditions can also be set up for the constraining points. Solution of these equations results in slight modification of the parameters.

3 Computers in Railways 73 The sets of unique parameters for the straight line, arc, and clothoid elements are: 1 length of a straight line R, 1 and arc length 1, Rp, Rf clothoid parameter and radii of the arcs of the preceding and following element If the coordinates of the starting point are given, together with its tangential bearing, the alignment is uniquely defined by the above parameters. Any additional geometrical specification overdetermines the alignment. This is especially true for the coordinates of the endpoint and the tangential bearing to the alignment there. In such a case, three conditions exist to ensure that the given endpoint coordinates and tangential bearing, are equal to those specified using functions of the above parameters. Minimizing the residuals of all or of part of the alignment parameters, while enforcing the three conditions, results in a consistent solution for all parameters. The equations (1) are valid for the alignment of a section between point a and point b, with coordinates xa, ya, xb, yb and tangents ta, tb: x& + f(parameters) = x& Ya + f (parameters) = y^ t& + f(parameters) = t& (I) The conditions define a non-linear system of condition equations, formulating consistency requirement for the alignment. Linearizing the functions fusing available initial values, a substitute linear system results. This can be solved by minimizing the weighted squared sum of parameter residuals in a least squares scheme. In this approach only 3 equations have to be solved. Enforcing the constraints leads to one additional equation - structured in a similar way - for each point. Because of the number of constraining points being small with respect to the number of parameters, the system of equations to be solved is also small. The approach is characterized by simultaneously solving for all parameters as candidates to be modified, and only giving preference to those required. An individual cofactor value allows one to influence the result. In addition it has the following optimisation properties: Cofactor 0 for parameter i enforces the residual of i to be zero. A singular cofactor submatrix for some parameters enforces a functional dependency of those parameters. Automatically modified cofactors lead to a powerful optimisation concept on the basis of penalty-functions. The algorithmic approach may also be seen as a finite element approach. The elements straight line, arc and transition clothoid curve are regarded as discrete elements.

4 74 Computers in Railways The effect of the strategy may therefore be described with the following model: Imagine apretensioned steel wire. Span the wire between the start- and endpoint of the alignment applying minimal bending energy. Bend the wire again with minimum bending energy, in order to fulfil the compulsory points requirements. The strategy has been realised in program system AXTRAN and integrated into VERM.ESN (Adelt, 1992). 3 Consistent Data Management and User Requirements The Data The first step in a database design consists of an appropriate analysis of the structure of the data which is to be managed. The data used in a rail system database may be subdivided into two groups: Geometrical data Topological data The geometrical data consists of: Information with respect to the track alignment's representative points (Horizontal coordinates, Height, Benchmark type,...) Information with respect to the rail elements (Starting and ending points, Element type, Element parameters) The topological data consists of: Rail connectivity Logical information with respect to the direction dependent usability of rail switches Railway routes as a sequence of preselected connections Management information with respect to the actual use such as the names of sequences; names of line connections; names and types of switches.

5 Computers in Railways 75 Rail Geometry "7\ /T v j "X v / ""*" straight r Rail Topology Figure 1: Relations between rail geometry and rail topology Figure 1 demonstrates the relationship between the topological and geometrical information. Any rail geometry may be modelled topologically in the above described way. The inverse task is, however, non-uniquely defined, since it is possible for multiple rail geometries to be modelled with exactly the same topology. The relationship mappings between geometry and topology are of type n:l. The topology results from the geometrical information by abstraction of the metric information. Metric information always relates to individual points, such as coordinates and heights; or to elements (radius, length,...). The Logical Data Model The data must be modelled in a systematic way in the logical data model. Due to the complex task of maintaining consistency requirements for different types, it proves reasonable to subdivide the database into geometrical and topological planes.

6 76 Computers in Railways Figure 2: Logical data model Relations Between the Geometrical and Topological Data Modelling access to the geometrical data from a topological area description, and the reverse task of accessing topological data from the area of the geometrical data is feasible if the access path is supported by suitably chosen support keys. On the other hand a strict separation of topological data and geometrical data has to be observed in order to maximise data integrity and consistency. The topological data may be organised in two main database structures: The track nodes database The track links database A representative geometrical point may be attached to each logical track node. The geometry of the representative starting point for logical node "track switch" would provide the necessary information for geometrical access to the switch. The data structure of the track nodes contains the names of the nodes and the address of the representative point. It is therefore possible to get access to the coordinates and the height of the representative point through the node name. Data sets from the track links database always contain the nodal names of the starting and ending nodes; the number of the track and an ordered sequence of point addresses. The point addresses belong to the starting and ending points of a sequence of geometrical elements which can be attached totally, or only partly, to an individual link of the track. Due to the approach described above, elements do not need to be split into two or more elements of the same geometry. Unique access to the correct geometry is still guaranteed via the topological information and vice versa.

7 Computers in Railways 77 The Database Structure The database data sets should be structured in such a way that the resulting relations will closely mirror the characteristics of the data to be managed. Fig. 3 shows a feasible structure for a rail database. The data are attached to the logical planes (geometry, topology, line data). The diagram shows the data sets in the shape of boxes, while the access keys relating the data sets are represented by ellipses. The arrows delineate the access paths. Railway Line Data V Chainage.} Chainage / Rail Nodes ~]{.,; "^Node ID ) ^ P Topology Point ID Point ID Points Elements r^ i U Descriptions /\ \/ x,y Positions \/ z Positions Superelevation Reference Line s Geometry Legend: Key Figure 3 Database structure Data Consistency The most essential aspect of the data management procedure is the maintenance of data consistency. Each modification of the data may be subject to a blunder. Data consistency checks must therefore be incorporated into the model. Consistency can only be checked if a certain level of redundancy is implicit in the data. This requirement is in contradiction to the case of standard database applications, where redundancy is only allowed for key attributes. Such data, however do not reflect the extremely high internal geometrical dependency of complex objects in engineering, which is especially obvious in railway management.

8 78 Computers in Railways A prerequisite of any consistency check is a complete definition of consistency conditions. For the purpose of consistency checking, our track alignment database may be classified according to three criteria: 1. The database to which it relates 2. The degree of interrelation and interdependence of the data to which it relates (within a data set, within a data base connecting data bases) 3. The geometry and topology Some essential conditions for consistency are as follows: The data correspond to the defined areas of allowable values (static condition); Each point may exist in the database only once, though it may have several coordinate values or be expressed in several coordinate systems; Combinations of starting and end points are uniquely defined in the elements database; Adjacent elements connect to each other smoothly in a permissible way; The distance between the same pairs of points in different data bases are always equal;... 4 Conclusion It has been shown that complex engineering structures such as railway lines require high precision surveying. Reliable geometry and consistent data management are the basis for all subsequent work. Unusual and flexible solutions have to be taken into account to achieve this goal. For a description of rail geometry in a global coordinate system, data management is most essential in order to guarantee a consistent data bank. This is especially true for updated situations with complex geometrical interdependancy of the data. The concept proposed above is based on an information system in which the three dimensional data of all rails is entered together with the results from the periodic surveys. The system is not only suited for regional rail management but also for all municipal rail related tasks like subways and trams, where local modifications due to construction activities require reliable, complete and fast answers. It may additionally be extended to road alignment tasks, or to the alignment of special tracks for city buses and trolly buses. New train mounted dynamic monitoring devices enable tilt and inclination data to be logged every 25cm along existing tracks. The authors have proposed the evaluation of such data in order to derive the actual state of the rail geometry. Initial results have proven to be very promising although huge amounts of data are involved which has to be properly managed. If additional ground control is available, the alignment parameters so derived are of millimetre magnitude. This approach will therefore increasingly replace current surveying practice.

9 References Computers in Railways Adelt,H. (1992): 'VERM.ESN Vermessungsprogramm fur gleistechnische Anlagen', technet Berlin 2. Grundig, L. (1981). 'Program system AXOPT for designing highways,' PTRC Summer Annual Meeting, Warwick. 3. Grundig, L. and Bahndorf, J. (1988). 'Bin rechnergestiitztes Entwurfssystem zur dreidimensionalen Trassierung,' X. Internationaler Kursfur Ingenieurvermessung, Miinchen, September, D7. 4. Grundig, L. (1988).'Datenverwaltungskonzepte fur typische Aufgaben aus der Ingenieurgeodasie,' DGKReihe C, Nr. 336, Munchen. 5. Grundig, L. (1990). "Ein System zur Trassierungsberechnung,' Vermessung, Photogrammetrie Kulturtechnik, Vol. 12., Zurich. 6. Grundig, L. (1991). 'Recent developments with respect to the automated processing and analysis of engineering survey data,' 7, Grundig, L., Bahndorf, J. and Singer, P. (1992). 'The design and management of the three dimensional alignment of rails and switches using RAILCAT,' Comp' Rail 92 Proceedings of an International Symposium, Washington. 8. Grundig, L., Bahndorf, J. and Gielsdorf, F. (1993a). Konzeptfur den Aufbau einer Datenbank zur Verwaltung von geometrischen und topologischen Daten von Gleisanlagen der Deutschen Bundesbahn, Deutsche Bundesbahn Internal Report. 9. Grundig, L., Aschoff, B., Milev, I. and Bahndorf, J. (1993b). Integration of GPS and engineering survey measurements,' XII. Int. Symposium on Deformation Measurements, Banff, Canada 1993